HOW TO FIGURE AVERAGES.
Decimals are Best.—Divide total points by total innings. Thus, 300 points in 28 innings show 1020
28 in crude fractions, 10 and 5/7ths in the lowest evenly reduced ones, and 10.71 (71/100ths) decimally. The first system seldom gives an accurate idea at sight. In the second, the fractions cannot always be reduced evenly, as above. Ordinarily, the third is closest, briefest and clearest.
Avoid a Jumble.—Some computers mix themselves and others up by using all three methods. Others, as a convenience, express the single average as 1020
28, and the general average not as 8170
175, to be consistent, but as 8.97. This is akin to the barbarism of speaking in two languages at once. There are others who, simply because it is so divisible, convert the 8170
175 into 834
35, so that anybody seeking to prove the average by finding the points and innings will have rare figuring as a preliminary.
Decimalizing.—This is simply adding a cipher to the right-hand end of every remainder after the dividend has no unused figure left. Adding a cipher to the 20 in 1020
28 yields 7 and 4 over when divided by 28, and now adding a cipher to the 4 will result altogether in 10.71, with 12 over.
Pay no attention to this remainder unless, if a general average, 10.71 seems to be a tie with some other general average. Such a tie will rarely happen. Should it, add a cipher to the 12, and dividing the 120 by 28 will result in 10.714 (1000ths now, instead of 100ths), with 8 over. If there is still a tie, proceed as before, first making 80 of the 8.
Give and Take.—Had the 10.71’s remainder been 14 or more, instead of 12, which is less than one-half the innings, the average would change to 10.72. The arbitrary rule is to ignore the final remainder when it is less than half the innings, but enlarge it and give it to the player when it is half or more.
Reconversion.—If for any reason it be necessary to find the number of innings, add ciphers (two will usually be enough in billiards) to the points, and divide by the decimalized average. Thus 1071)30000(28 innings, with 12 over. To find the points on which a general average is based, innings (50) and average (16) being known, multiply the one by the other—16 × 50 = 800.
General Average.—A match of continuous points has but one average, whether it be played in one session or half a dozen; but it is different both in a tournament and in a match of several separate games, a majority to win.
In computing the general average, avoid the easy error of adding all a player’s game-averages together, and dividing the product by the number of games. There is only one condition in which this will show the true average, and that is when all the games have innings separately equal in number, howsoever much the points themselves may vary.
Illustration of false and true:
| Inn. | Points. | Game Average. |
|---|---|---|
| 15 | 600 | 40 |
| 30 | 600 | 20 |
| 30 | 600 | 20 |
| 7 | 600 | 85.71 |
| 82 | 82)2400(29.29 | 4)165.71(41.43 |
The average found by dividing by the number of games is grossly extravagant.
Losing Averages.—Properly, the loser’s average can never be higher than the winner’s. To concede that it can is to premiumize its maker’s inefficiency. Setting out to win the opening shot, he had failed, which is the only way, with fewer points, to make the seemingly higher average. It is equally unfair, in a continuous game of several sessions, to concede an average for a fraction of the game. By getting far behind, one player is without limit on any night, while the other is stopped every night by reaching the number of points assigned to every leader.
Except as personal compliments, losing averages are valueless. Their apparent makers do not wholly make them. Much depends upon the other man. The loser reaches a high figure largely because, having aimed to cover a given number of points, he failed to do so. It has often happened that a player with 50 to go has needed as many innings to make them as he had taken to make his other 250. As a rule, losers “let down” near the finish more than winners, and hence their average is dependent less upon themselves than upon those who close the game.